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**Algebra I/Data Analysis: Midterm Review Packet Unit 1: Relationships between Quantities and Reasoning with Equations **

**Part 1:** **Linear and Exponential Expressions**

*Write an expression to represent each of the following scenarios. *

1.

Julia purchases a lawn mower for $250. She plans to mow lawns to earn money and will charge $15 per lawn. 2.

Ricardo has $3,400 in the bank. It is collected interest at a rate of 1.5% per year. 3.

Kim is shopping on Black Friday for shoes. All shoes are half priced, and she has a coupon for an additional $15 discount on her entire purchase. 4.

Mark needs to find an expression for both the perimeter and area of the rectangular pig pen below. *x* + 2 3*x* 2 – 5

*Write a real-world scenario for each of the following expressions. *

5. 5

*x*

100 6. 2,000(3)

*x Simplify each of the following. *

7. 3(2

*x*

9) 2(4

*x*

1) 8. 2(9

*x*

2

*x*

) (4

*x*

2 2

*x*

) 9. (8

*x*

4

*y*

2 )(2

*x*

3

*y*

) 10. 5

*a*

8

*b*

10

*a*

3

*b*

5 11. (4

*x*

5

*y*

3

*z*

0 ) 2 (2

*xy*

) 12. 9

*p*

2

*q*

4 3

*p*

6

*q*

**Part 2: Relationships in One Variable **

*Solve each of the following for the unknown. Graph the solutions on a number line, where necessary. *

13. Tatiana needs to save $575 for car insurance. She already has $135 in her bank account from her birthday. If Tatiana earns $8 per hour working at Foot Locker, how many hours must she work to afford the insurance?

14. The Class of 2016 is fundraising for Prom. They have purchased t-shirts for $250 and plan to sell them for $12.50 each. How many shirts do they need to sell if they want to make $500 profit? 15. Jane wants to buy supplies for her daughter’s birthday party, but she wants to spend no more than $100. The cake is costing her $43, but she also wants to buy goody bags for all of the guests. If the goody bags are on sale for $4.95 each, what is the maximum number of guests she can afford? 16. 2

*x*

5 5

*x*

10 21. 5

*x*

7 2

*x*

28 18. 2(3

*x*

6) 5

*x*

6 2

*x*

22. 2

*x*

9

*x*

5

*x*

5 20. 2(3

*x*

4) 4 23. 5

*x*

6 2

*x*

15

**Part 3: Relationships in Two Variables **

24. Find the key features listed for the relationship below. Domain: __________________________ Range: ____________________________ Maximum: _______________________ Minimum: _______________________ Zero(s): __________________________ *y* – intercept: _____________________ 25. 26.

*x y x y *

2 3 5 2 -1 0 7 0 1 -5 9 2 2 7 11 17

*Fill in the following chart, giving or describing and example of each representation for the various function families. Fill in the bottom row with another family you have studied this year. *

Family Algebraic Example Graphical Example Pattern/Table Example

*f*

(

*x*

) 3

*x*

2

**Unit 2: Linear and Exponential Relationships Part 1: Representing Linear and Exponential Functions **

*Find a linear equation for each set of information.* 28. Jerry wants to lose 3 pounds of weight per month because he wants to wrestle at a lower weight class during his club season. His current weight is 210. 29. (9, 1) and (7, 5) 30.

*x *

y -3 -1 5 13

*Find the next two terms in each pattern, and label it as linear or exponential. *

31. 4, -2, -8, -14, ____________, _____________ 32. 162, 54, 18, 6, _____________, _____________

*Fill in the following graphic organizers. *

33.

*x* 0 1 2 3 4 5 6 7 8 *f*(*x*) 35 32 39 26 23 20 17 14 11

*Is the above function linear or exponential? How do you know? *

34.

850 students currently attend Small Town High School. The Board of Education predicts that Small Town High School will increase its population by about 5% each year.

*x* *f*(*x*)

*Is the above function linear or exponential? How do you know? *